Nitorgen doped silicon wafer and manufacturing method thereof

ABSTRACT

An epitaxial wafer and a high-temperature heat treatment wafer having an excellent gettering capability are obtained by performing epitaxial growth or a high-temperature heat treatment. A relational equation relating the density to the radius of an oxygen precipitate introduced in a silicon crystal doped with nitrogen at the time of crystal growth can be derived from the nitrogen concentration and the cooling rate around 1100° C. during crystal growth, and the oxygen precipitate density to be obtained after a heat treatment can be predicted from the derived relational equation relating the oxygen precipitate density to the radius, the oxygen concentration, and the wafer heat treatment process. Also, an epitaxially grown wafer and a high-temperature annealed wafer whose oxygen precipitate density has been controlled to an appropriate density are obtained, using conditions predicted by the method.

TECHNICAL FIELD

The present invention relates to a method for manufacturing a siliconwafer with controlled crystal defects, obtained by growing a siliconsingle crystal ingot from molten silicon doped with nitrogen and cuttinga wafer from it, and a silicon wafer obtained by this method.

BACKGROUND ART

With the trend towards higher levels of integration and furtherminiaturization of a semiconductor circuits, crystal defects formed atthe time of crystal growth existing near the surface layer of a siliconwafer can have a great effect on device performance. In general, crystaldefects that degrade device characteristics are of the following threekinds.

1. Void defects that occur as a result of aggregation of vacancies

2. Oxidation Induced Stacking Faults (OSF)

3. Dislocation clusters that occurs as a result of aggregation ofinterstitial silicon

In order to obtain a silicon wafer that does not include the abovecrystal defects formed at the time of crystal growth near the surfacelayer where a device circuit is manufactured, the following methods havebeen devised.

1.) To manufacture defect-free single crystal ingots by controlling thecrystal growth conditions

2.) To eliminate void defects near the surface layer of the wafer byhigh-temperature annealing

3.) To grow a defect-free layer on the surface of a wafer by epitaxialgrowth

Although the above methods 1) to 3) can prevent the problem of crystaldefects, none of these methods is necessarily preferable for the controlof oxygen precipitates. Because oxygen precipitates (bulk micro defect:BMD) play an important role as gettering sites against harmfulheavy-metal contamination incidentally occurring in the device circuitmanufacturing process, they are preferably generated at an appropriatedensity in the heat treatment in the device circuit manufacturingprocess. However, the conditions selected for restricting crystaldefects in the above methods 1) to 3) are often disadvantageous for thegeneration of BMDs. To begin with, BMD control in 1), 2) and 3) isdescribed.

When a defect-free single crystal ingot in 1) is to be manufactured, theoxygen concentration needs to be lowered to prevent OSFs from occurring.However, under a low oxygen concentration conditions, it is difficult toobtain sufficient BMD density by a normal heat treatment. Also, thecrystal in the defect-free single crystal ingot is in a state wherein avacancies-dominant defect-free portion and an interstitialsilicon-dominant defect-free portion coxexist in a radial direction, andthe oxygen precipitate characteristics are totally different betweenthese portions. Accordingly, a post-treatment to ensure uniform oxygenprecipitate characteristics within the silicon wafer surface is need dinsome cases. As a post-treatment for uniform oxygen precipitatecharacteristics, a method of eliminating such precipitatecharacteristics in an as-grown state by a rapid high-temperature heatingtreatment has been proposed (for example, Patent Documents 1 and 2).Also, a method to make uniform the BMD density by a heat treatment thatstrongly effects nuclear generation on the low-temperature side that isnot influenced by the dominant point defect kind has been proposed (forexample, Patent Document 3 and 4). However, the former method requires arapid high-temperature heating treatment, which is a high-cost process,and the latter method requires a long-time heat treatment process, bywhich it is possible to density and make uniform the BMDs but it is verydifficult to control the density to a selected density. Thus, thedefect-free single crystal ingot is actually used only for limitedapplications that do not require gettering by the BMDs.

Next, a high-temperature annealed wafer in 2) is described. Void defectsnear the surface are eliminated by a heat treatment typically for onehour at 1200° C. under a non-oxidizing atmosphere such as hydrogen andargon. However, the voids in a normal crystal that are eliminated byannealing are only those on the outermost surface layer of the wafer,and in order to create a void defect free area deeper than the devicemanufacturing area, it is very important to minimize the size of thevoids so that they can be eliminated easily (for example, PatentDocument 5 shown below). However, in order to create a void defect freearea that is deep enough, merely minimizing the void defects is notsufficient, but lowering the oxygen concentration is also stronglydesired (for example, Non-Patent Document 1 shown below). This isbecause the inner wall of the void is covered with an oxide film in anas-grown state, and the shrinkage of the void defects starts after theinner wall oxide film is dissolved and eliminated. That is, as the depthwhich is sufficient for the inner wall oxide film to be dissolved andeliminated by the oxygen outward diffusion effect depends on the oxygenconcentration of the crystal, the depth is shallow in crystals with ahigh oxygen concentration. Thus, in order to obtain a sufficient voiddefect free layer depth, lowering the oxygen concentration of thecrystal is very important. However, it is generally difficult for acrystal with a low oxygen concentration to have sufficient BMD density.

Further, an epitaxially grown wafer in 3) is described. The epitaxiallygrown wafer is advantageous in the voids present in the substrate waferare not transcribed on the epitaxial layer, and a defect-free siliconlayer can be obtained on the surface layer. However, since the wafertemperature is raised in a short time to a high temperature forepitaxial growth in consideration of the productivity, as-grown micronuclei that becomes BMD nuclei disappear, and it is very likely thatsufficient BMD density will not be obtained even if a heat treatment isapplied thereafter.

In consideration of the above described situation concerninghigh-temperature annealed wafers and epitaxial wafers, a method ofnitrogen doping has been proposed. First, the effect of nitrogen dopingon the high-temperature annealed wafer is described. Using a crystalwhose void defect size has been reduced by doping nitrogen as a crystalfor high-temperature annealing has been proposed (for example, PatentDocument 6 shown below). Also, although it is traditionally known thatabnormal BMDs are generated in nitrogen-doped CZ silicon crystals, ithas been shown that controlling the nitrogen concentration can result inBMDs with appropriate density (for example, Patent Document 7 shownbelow). This document shows that 1×10⁹ units/cm³ or more BMD density canbe obtained when the nitrogen concentration of even a crystal with lowoxygen concentration is set to 1×10¹³ atoms/cm³ or more. Many similarinventions to this exist, but they describe only the nitrogenconcentration as a factor to control the BMD density of ahigh-temperature annealed wafer (for example, Patent Documents 7, 8, 9and 10 shown below). However, the BMD density is determined not only benitrogen concentration but by the temperature increase rate in eachtemperature range at the time of high-temperature annealing (forexample, Patent Document 11 shown below). However, the range defined inthis document includes all condition ranges to be selected generally,and this document does not disclose a method for controlling the BMDsindividually. Also, a method of obtaining an appropriate BMD density byperforming annealing for 60 minutes or more at a temperature of 700° C.or more and 900° C. or less as a heat treatment before high-temperatureannealing or by setting the thermal annealing rate in a temperaturerange from 700° C. or more to 900° C. or less to 3° C./minute or less inthe thermal annealing step of high-temperature annealing has beenproposed (for example, Patent Document 12 shown below). However, theBMDs are not controlled only by this definition, and a comprehensivemethod for controlling the BMDs has not been disclosed.

Next, a nitrogen doping technique proposed for an epitaxially grownwafer is described. As for the epitaxially grown wafer, it is likelythat oxygen precipitate nuclei will disappear in the epitaxial growthprocess. In contrast, it if shown that 5×10³ units/cm³ or more BMDdensity is observed even after epitaxial growth when doping with 1×10¹³atoms/cm³ or more nitrogen (for example, Patent Document 13 shownbelow). this may be because, in the nitrogen-doped crystal, generationof as-grown nuclei starts during crystal growth at a higher temperaturethan in a normal crystal, and they grow at the high temperature and formlarge-sized nuclei. It is thought that these large-sized nuclei do notdisappear even in the epitaxial growth process. However, this BMDdensity is not necessarily preferable. It is shown that, although theBMD density after epitaxial growth is greatly influenced by nitrogenconcentration, is also influenced by the annealing process time at ahigh temperature before the epitaxial growth process (for example,Patent Document 14 shown below). The annealing process before theepitaxial growth means an H₂ or HCl baking process at an equal or highertemperature than the epitaxial growth temperature generally for thepurpose of elimination of natural oxide films. Meanwhile, it is shownthat the BMD density observed after the epitaxial growth is influencedby the cooling rates in two temperature ranges, that is, a cooling ratefrom 1150° C. to 1020° C. and a cooling rate from 1000° C. to 900° C.,in the crystal growth process (for example, Patent Document 15 shownbelow). The effects of the cooling rates in the two temperature rangesare as follows. The temperature range from 1150° C. to 1020° C. is atemperature range for the generation and growth of void defects, andsince rapid cooling in this temperature range restrains the absorptionof vacancies in voids, the concentration of residual vacancies israised, and subsequent BMD nucleus generation is promoted. Thetemperature range from 1000° C. to 900° C. is regarded as a temperaturerange in which the BMDs are generated in a nitrogen-doped crystal, andslow cooling in this temperature range increases the BMD density,according to this document. This document recommends that the coolingrate from 1150° C. to 1020° C. be 2.7° C./minute or more, and thecooling rate from 1000° C. to 900° C. be 1.2° C./minute or less, inorder to obtain sufficient BMD density. However, it says the effect ofthe cooling rate in the temperature range from 1000° C. to 900° C. isslight, and the effect of the cooling rate from 1150° C. to 1020° C. issignificant. However, the relation of these with the nitrogenconcentration and other factors is not described clearly (PatentDocument 15 shown below). It has been proposed that the BMD densityafter the epitaxial growth is further controlled by performingpre-annealing for 15 minutes or more and 4 hours or less at atemperature of 700° C. or more and 900° C. or less before the epitaxialgrowth process (for example, Patent Document 16 shown below).

As described above, it is clear the BMD density of a nitrogen-dopedsilicon wafer after the epitaxial process depends on 1) the nitrogenconcentration, 2) the crystal thermal history, 3) the temperature andtime of a high-temperature heat treatment performed for elimination ofnatural oxide films in the epitaxial process, 4) the temperature andtime of pre-annealing performed before the epitaxial process, and 5) theoxygen concentration, as a matter of course.

The BMD density of a nitrogen-doped silicon wafer after thehigh-temperature annealing process depends on 1) the nitrogenconcentration, 2) the crystal thermal history, 3) the thermal annealingrate during the high-temperature annealing process, 4) the temperatureand time of pre-annealing performed before the high-temperatureannealing process, and 5) the oxygen concentration. Although it is knownthat the BMD density depends on these many factors simultaneously, theeffect of these factors has only partially been clarified, as describedabove. As the nitrogen has a small segregation coefficient in thenitrogen-doped crystal, the nitrogen concentration exhibits significantchanges in the axial direction of the crystal. Also, as the BMDs of thenitrogen-doped crystal depend on large as-grown oxygen precipitatenuclei generated in the cooling process during the crystal growth, theyare strongly influenced by the thermal history during crystal growth.The growth process of the as-grown nuclei to visible size stronglyinfluenced by nitrogen concentration and thermal history have not beenclarified, and thus it has been conventionally necessary to control thenitrogen doping amount and the heat treatment process for obtaining anappropriate BMD density for each crystal growth condition and for eachprocess.

Patent Document 1: Japanese Unexamined Patent Application PublicationNo. 2001-503009

Patent Document 2: Japanese Unexamined Patent Application PublicationNo. 2002-299344

Patent Document 3: Japanese Unexamined Patent Application PublicationNo. 2000-264779

Patent Document 4: Japanese Unexamined Patent Application PublicationNo. 2002-134517

Patent Document 5: Japanese Unexamined Patent Application PublicationNo. H10-208987

Patent Document 6: Japanese Unexamined Patent Application PublicationNo. H10-98047

Patent Document 7: Japanese Unexamined Patent Application PublicationNo. 2000-211995

Patent Document 8: Japanese Unexamined Patent Application PublicationNo. H11-322491

Patent Document 9: Japanese Unexamined Patent Application PublicationNo. 2001-270796

Patent Document 10: Japanese Unexamined Patent Application PublicationNo. 2001-284362

Patent Document 11: Japanese Unexamined Patent Application PublicationNo. 2002-118114

Patent Document 12: Japanese Unexamined Patent Application PublicationNo. 2002-353225

Patent Document 13: Japanese Unexamined Patent Application PublicationNo. H11-189493

Patent Document 14: Japanese Unexamined Patent Application PublicationNo. 2000-044389

Patent Document 15: Japanese Unexamined Patent Application PublicationNo. 2002-012497

Patent Document 16: Japanese Unexamined Patent Application PublicationNo. 2003-73191

Non-Patent Document 1: K. Nakamura, T. Saishoji, and J. Tomioka; The63^(rd) JSAP (The Japan Society of Applied Physics) Annual MeetingDigest, Autumn 2002; P. 381; No. 1 24p-YK-4

DISCLOSURE OF THE INVENTION

Problems to be Solved by the Invention

It is an object of the present invention to provide a wafermanufacturing method to obtain an epitaxial wafer and a high-temperatureheat treatment wafer having a high gettering capability by applying anappropriate heat treatment process to a silicon wafer cut from a singlecrystal ingot doped with nitrogen in a process of growing asemiconductor silicon single crystal and thereafter performing anepitaxial growth or a high-temperature heat treatment.

The BMD density of a nitrogen-doped silicon wafer after the epitaxialprocess depends on 1) the nitrogen concentration, 2) the crystal thermalhistory, 3) the temperature and time of a high-temperature heattreatment performed for elimination of natural oxide films in theepitaxial process, 4) the temperature and time of pre-annealingperformed before the epitaxial process, and 5) the oxygen concentration.The BMD density of a nitrogen-doped silicon wafer after thehigh-temperature annealing process depends on 1) the nitrogenconcentration, 2) the crystal thermal history, 3) the temperatureincrease rate during the high-temperature annealing process, 4) thetemperature and time of pre-annealing performed before thehigh-temperature annealing process, and 5) the oxygen concentration.Although it is known that the BMD density depends on these many factorssimultaneously, the effect of these factors has only partially beenclarified, as described above. Thus, it is extremely difficult todetermine the conditions for obtaining a BMD density with sufficientgettering capability (e.g., 5×10⁸ units/cm³) at a good yield ratio. Thepresent invention proposes a method for deriving a relational equationrelating the density to the size of a BMD introduced in a siliconcrystal doped with nitrogen at the time of crystal growth from nitrogenconcentration and a cooling rate around 1100° C. during crystal growth,a method for predicting the BMD density to be obtained after a heattreatment from the derived relational equation relating the BMD densityto the radius, oxygen concentration, and the wafer heat treatmentprocess, and a method for manufacturing an epitaxially grown wafer and ahigh-temperature annealed wafer whose BMD density is controlled to havean excellent gettering capability be using the method.

Means for Solving the Problems

It is thought that large as-grown oxygen precipitate nuclei exist in anitrogen-doped crystal, and as they are stable under high temperature,they act as BMD nuclei in epitaxially grown wafers and ahigh-temperature annealed wafers. The present invention proposes amethod for deriving a relational equation relating the density to theradius of an oxygen precipitate introduced in a silicon crystal dopedwith nitrogen at the time of crystal growth form the nitrogenconcentration and the cooling rate around 1100° C. during crystalgrowth, a method for predicting the oxygen precipitate density to beobtained after a heat treatment from the derived relational equationrelating the oxygen precipitate density to the radius, oxygenconcentration, and a wafer heat treatment process, and a method formanufacturing an epitaxially grown wafer and a high-temperature annealedwafer whose oxygen precipitate density has been controlled to anappropriate density, using conditions predicted by the method.

First, a method for deriving a relational equation relating the densityto the size of an oxygen precipitate introduced in a silicon crystaldoped with nitrogen at the time of crystal growth from the nitrogenconcentration and the cooling rate around 1100° C. during crystal growthis described. In order to derive the relational equation, the followingexperiment was performed.

First, crystals with various nitrogen concentrations grown with variousthermal histories were prepared. They were heated to a predeterminedtemperature by a rapid thermal annealing apparatus, and afterprecipitates smaller than a critical nucleus radius to exist at thetemperature were eliminated, they underwent a heat treatment for 4 hoursat 300° C. and thereafter a heat treatment for 16 hours at 1000° C., andnuclei remaining after the rapid thermal annealing process were grown toan observable size by the heat treatments. It is well known that nonucleus is generated in a CZ silicon crystal under a heat treatment at900° C. or higher, and the BMD density that became apparent after thetreatment for 4 hours at 900° C. and the treatment for 16 hours at 1000°C. is the density of the BMDs remaining at the temperature reached bythe rapid thermal annealing apparatus, that is, the density of thenuclei larger than the critical nucleus radius at the heatingtemperature among the as-grown nuclei. Thus, by evaluating the relationbetween the heating temperature during rapid thermal annealing and thedensity observed after this process, the size distribution of theas-grown nuclei can be predicted. FIG. 1 shows the relation between aheating temperature and BMD density when the oxygen concentration is12×10¹⁷ atoms/cm³, and when the nitrogen concentration is changed underthe same growth conditions. It shows that the higher the nitrogenconcentration is, the higher the BMD density is, and it also shows theBMD is still stable at higher temperatures. Next, a method for derivingthe size distribution of the as-grown nuclei form the data in FIG. 1 isexplained.

In general, the relation between the heating temperature and a criticalnucleus radius is expressed by Equation 1).

Equation 1Rcri=2σΩ/k_(B)T ln (Co/Co^(eq))   1)

Rcri is a critical nucleus radius, σ is the surface energy between SiO₂and silicon, Ω is volume of SiO₂ per oxygen atom, k_(B) is the Boltzmannconstant, T is the absolute temperature, Co is the oxygen concentration,and Co^(eq) is the thermal equilibrium concentration of oxygen. If thetemperature on the horizontal axis in FIG. 1 is replaced with thecritical nucleus radius by Equation 1), FIG. 1 will show the sizedistribution of the as-grown nuclei. However, it is not necessarilyproper to directly replace the temperature on the horizontal axis inFIG. 1 with the critical nucleus radius. This is because the as-grownnuclei in the nitrogen-doped crystal are extremely large, even thenuclei smaller than the critical nucleus radius may remain because theytake time to disappear, and not all the remaining nuclei are as-grownnuclei larger than the critical nucleus radius. Then, a processsimulation of the heating experiment in FIG. 1 was performed, and theradius of the nuclei that can remain in the experiment at each settemperature was derived by numerical calculation. The method ofnumerical calculation is shown below. The change in the radius of theprecipitate during the process when a precipitate having an arbitraryinitial radius is heated in a temperature pattern in a heatingexperiment was numerically calculated using Equation 2) and 3).

Equation 2dR/dt=DΩ (Co-Co¹)/R   2)Equation 3Co¹=Co^(eq) exp (2σΩ/Rk_(B)T)   3)

Equation 2) expresses the rate of change of the radius, where R is theradius of the precipitate, D is the diffusion coefficient of oxygen, andCo¹ is the oxygen concentration at the interface of the precipitate,which is expressed by Equation 3). The minimum initial radius of anucleus that does not disappear during the process when the calculationis carried out using these equations by setting the oxygen concentrationand the temperature pattern and giving several initial radii has beendefined as a process critical nucleus radius. The relation between thederived process critical nucleus radius and the BMD density is shown inFIG. 2. FIG. 2 shows the relation between the radius of an as-grownnucleus and the density of as-grown nuclei larger than the radius. Itcan be seen from FIG. 2 that the size distribution of the as-grownnuclei for each nitrogen concentration shifts in parallel. It can alsobe seen that, although nuclei having a smaller radius have a higherdensity, this tendency is saturated at a certain value, and thesaturation density does not depend on the nitrogen concentration. Thisis explained as follows. Although FIG. 2 shows the relation between theradius of an as-grown nucleus and the total density of nuclei largerthan the radius, it is clear that this relation can be rewritten to therelation in FIG. 2 when the normal size distribution is to be shown.That is, the size distribution of the as-grown nuclei in thenitrogen-doped crystal shifts to larger sizes as the nitrogenconcentration increases, but a change in the total density is notobserved. This means that, although the higher the nitrogenconcentration, the higher the temperature at which the as-grown nucleiare generated, and thus the larger the size of the as-grown nuclei, buttotal density itself hardly changes. Next, nuclei whose density is notsaturated were selected from the data in FIG. 2, and the relation amongBMD density, nitrogen concentration, and the critical nucleus radius wasanalyzed using multivariate analysis. As a result, it was found that therelation is expressed as in the following equation.

Equation 4BMD=6.4 ×10⁻¹⁹N^(1.39)R^(−1.163)   4)

Where BMD is the density of as-grown precipitates (units/cm³), N is thenitrogen concentration (atoms/cm²), and R is the radius of the as-grownprecipitate. FIG. 4 shows a comparison between the calculated valuesbased on Equation 4) and the actual measured values. It can be seen fromFIG. 4 that the size distribution of the as-grown nuclei highlycorresponds to the size distribution predicted from Equation 4).

Next, the relation with thermal history during crystal growth is shown.A similar experiment to FIG. 2 was carried out using crystals withdifferent cooling rates in a temperature range for generation of voiddefects. While the cooling rate of the crystal around 1100° C. in FIG. 2is 4° C./minute, FIGS. 5 and 6 show the relation between the criticalnucleus radius and the BMD density in wafers with various nitrogenconcentrations, setting the cooling rate of the crystal around 1100° C.to 1.5° C./minute and 2.0° C./minute, respectively. Each line shown inthe figures is a calculation line derived by applying the correspondingnitrogen concentration amount to Equation 4) and is shown forcomparison. It can be seen from the comparison with the calculationlines that Equation 4) is applicable regardless of the cooling rate ofthe crystal. Meanwhile, the saturation BMD density is lower as thecooling rate of the crystal is lower. The present inventors analyzed therelation between the saturation density and the cooling rate of thecrystal further in detail and it is shown in FIG. 7. The relation inEquation 5) was found from FIG. 7.

Equation 5Saturation BMD density=7.5×10⁸ CR^(1.5)   5)

Where CR is the cooling rate around 1100° C. during crystal growth (°C./minute). It is reported that the density of any defect, related toaggregation reaction of point defects, such as a void defects,interstitial silicon-type dislocation clusters and OSFs, is proportionalto the cooling rate to the 1.5^(th) power. The relationship to a coolingrate to the 1.5^(th) power is thought to be a characteristic whennucleus generation is rate-controlled by the consumption offast-diffused point defects. It can be seen from Equation 5) that thecooling rate must be 0.76° C./minute of faster in order for thesaturation BMD density to exceed 5×10⁸ units/cm³, which is a BMD densityexerting sufficient gettering effects. Although Patent Document 15states that the cooling rate from 1150° C. to 1020° C. needs to be 2.7°C./minute or faster in order to obtain a sufficient BMD density, it juststates that such a cooling rate is needed in a specific nitrogenconcentration and a specific epitaxial growth process.

Accordingly, it has become apparent that the relation relating thedensity to the size of an oxygen precipitate introduced in a siliconcrystal doped with nitrogen at the time of crystal growth can be derivedfrom the nitrogen concentration and a cooling rate around 1100° C.during crystal growth, using Equations 4) and 5).

Next, a method for predicting the oxygen precipitate density of anepitaxially grown wafer and a high-temperature annealed wafer to beobtained after a heat treatment from the derived relation is explained.As described above, the BMD density of a nitrogen-doped silicon waferafter the epitaxial process depends on 1) the nitrogen concentration, 2)the crystal thermal history, 3) the temperature and time of ahigh-temperature heat treatment performed for elimination of naturaloxide films in the epitaxial process, 4) the temperature and time ofpre-annealing performed before the epitaxial process, and 5) the oxygenconcentration. On the other hand, high-temperature annealing is aprocess attempting to eliminate void defects near the surface layer andis performed at a temperature of 1100° C. or higher, and the BMD densityof a nitrogen-doped silicon wafer after the high-temperature annealingprocess depends on 1) the nitrogen concentration, 2) the crystal thermalhistory, 3) a thermal annealing rate during the high-temperatureannealing process, 4) the temperature and time of pre-annealingperformed before the high-temperature annealing process, and 5) theoxygen concentration.

Then, by providing as initial values of the size and the density of theoxygen precipitates introduced in a silicon crystal doped with nitrogenat the time of crystal growth by Equations 4) and 5), and byprocess-simulating growth and disappearance of their as-grown nulcei ineach of the above heat treatment processes by Equation 2), the densityof the nuclei that remain after the processes can be derived. This is asimilar calculation to one to derive FIG. 2 from FIG. 1. By thiscalculation, the density of the as-grown nuclei that remain after anarbitrary heat treatment processes can be derived.

By these procedures, the conditions for exceeding 5×10⁸ units/cm³, whichis the BMD density exerting sufficient gettering effects, can beselected easily. As described above, setting the cooling rate of thecrystal at the time to 0.76° C./minute or faster is an importantcondition and is sometimes an essential condition.

Meanwhile, as for the physical parameters D and Co^(eq) used forcalculation, J. C. Mikkelesn Jr.'s values (J. C. Mikkelesn Jr.,Proceeding of Material Research Society Symposium, Vol. 59 (1986) p 19)were used. Also, Ω is 2.21×10⁻²³ cm³. As for σ, in the calculation inthe present invention, one that is the most appropriate for expressingdisappearance and growth of the BMD is selected from the results ofvarious process simulations performed before in consideration of thetemperature dependency. That is, σ=575 erg/cm² in the case of 800° C. orless, σ=575+325 (T° C.−800)/150 erg/cm² in the case of 800° C. or moreand 950° C. or less, σ=900 erg/cm² in the case of 950° C. or more and1020° C. or more and 1100° C. or less, and σ=730 erg/cm² in the case of1100° C. or more. As for the value σ, the value 310 erg/cm² is oftenused, but there is no established consensus about this, and there is apresumption that it is a very large value. However, if the same value isused for σ to be used to derive the size distribution of as-grown nucleiand for σ to be used to do a simulation regrading growth anddisappearance of the as-grown nuclei in the heat treatment processes,there is no significant change in the predicted BMD result after theheat treatment processes.

Effects of the Invention

The present invention proposes a method for deriving a relationalequation relating the density to the size of an oxygen precipitateintroduced in a silicon crystal doped with nitrogen at the time ofcrystal growth from the nitrogen concentration and the cooling ratearound 1100° C. during crystal growth, a method for predicting the BMDdensity to be obtained after a heat treatment form the derivedrelational equation relating the BMD density to the radius, the oxygenconcentration, and the wafer heat treatment process, and a method formanufacturing an epitaxially grown wafer and a high-temperature annealedwafer whose BMD density has been controlled 5×10⁸ units/cm³ or more tohave a sufficient gettering capability by using the method.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the relation between the heating temperature and the BMDdensity in wafers with various nitrogen concentrations.

FIG. 2 shows the relation between the radius of an as-grown nucleus andthe total density of nuclei larger than the radius.

FIG. 3 is a schematic diagram showing the nitrogen concentrationdependency of the size distribution of the as-grown nuclei.

FIG. 4 shows a comparison between the densities of as-grown nucleicalculated based on a prediction equation and actual measured values.

FIG. 5 shows the relation between the radius of an as-grown nucleus andthe total density of nuclei larger than the radius when the cooling rateof the crystal around 1100° C. is set to 1.5° C./minute.

FIG. 6 shows the relation between the radius of an as-grown nucleus andthe total density of nuclei larger than the radius when the cooling rateof the crystal around 1100° C. is set to 2.0° C./minute.

FIG. 7 shows the relation between the saturation BMD density and thecooling rate of the crystal around 1100° C.

FIG. 8 shows the relation between the BMD density and the nitrogenconcentration and time when the baking temperature in an epitaxialgrowth process is set to 1150° C.

FIG. 9 shows the relation between the BMD density and the nitrogenconcentration and time when the baking temperature in an epitaxialgrowth process is set to 1200° C.

FIG. 10 shows the relation between the BMD density and the nitrogenconcentration and time when the baking temperature in an epitaxialgrowth process is set to 1230° C.

FIG. 11 shows the relation between the BMD density and the nitrogenconcentration and time when the pre-annealing temperature before anepitaxial growth process is set to 750° C.

FIG. 12 shows the relation between the BMD density and the nitrogenconcentration and time when the pre-annealing temperature before anepitaxial growth process is set to 800° C.

FIG. 13 shows the relation between the BMD density and the nitrogenconcentration and time when the pre-annealing temperature before anepitaxial growth process is set to 850° C.

FIG. 14 shows the relation between the BMD density and the nitrogenconcentration and time when the pre-annealing temperature before ahigh-temperature annealing process is set to 750° C.

FIG. 15 shows the relation between the BMD density and the nitrogenconcentration and time when the pre-annealing temperature before ahigh-temperature annealing process is set to 800° C.

FIG. 16 shows the relation between the BMD density and the thermalannealing rate from 800° C. to 1000° C. in a high-temperature annealingprocess and nitrogen concentration.

FIG. 17A shows a manufacturing process of an epitaxial wafer used in theembodiments.

FIG. 17B shows a manufacturing process of an annealed wafer used in theembodiments.

FIG. 18A shows a general manufacturing process of a mirror finishedwafer.

FIG. 18B shows a general manufacturing process of an epi-wafer.

FIG. 19A shows the conditions and results of pre-annealing and epitaxialin Embodiment 5.

FIG. 19B shows other conditions in Embodiment 5.

FIG. 20A shows the conditions and results of pre-annealing and epitaxialin Embodiment 6.

FIG. 20B shows other conditions in Embodiment 6.

FIG. 21A shows the conditions and results of pre-annealing andhigh-temperature annealing in Embodiment 7.

FIG. 21B shows other conditions in Embodiment 7.

FIG. 22A shows the conditions and results of pre-annealing andhigh-temperature annealing in Embodiment 8.

FIG. 22B shows other conditions in Embodiment 8.

Explanations of the Numerals

S110: single crystal growing step

S120: processing step

S140: epitaxial step

S210: single crystal growing step

S220: processing step

S240: annealing step

PREFERRED MODE FOR CARRYING OUT THE INVENTION

The present invention proposes a method for deriving a relationalequation relating the density to the radius of an oxygen precipitateintroduced in a silicon crystal doped with nitrogen at the time ofcrystal growth from the nitrogen concentration and the cooling ratearound 1100° C. during crystal growth, a method for predicting theoxygen precipitate density to be obtained after a heat treatment fromthe derived relational equation relating the oxygen precipitate densityto the radius, the oxygen concentration, and the wafer heat treatmentprocess, and a method for manufacturing an epitaxially gown wafer and ahigh-temperature annealed wafer whose oxygen precipitate density iscontrolled to an appropriate density, using conditions predicted by themethod. Here, an appropriate oxygen precipitate density may mean apreferable or more preferable oxygen precipitate density based on theintended application of a silicon wafer to be manufactured. For example,for a silicon wafer for intrinsic gettering, the oxygen precipitatedensity is preferably 5×10⁸ units/cm³ or more, more preferably 8×10⁸units/cm³ or more, and further preferably 1×10⁹ units/cm³ or more.

The calculation method is as follows: the size distribution of as-grownoxygen precipitates is provided as an initial value by Equation 4).

Then, the growth and disappearance of the nuclei having individual radiiin the temperature processes in the epitaxial process andhigh-temperature annealing process are numerically calculated byEquations 2) and 3).

As a result, the density of the BMD nuclei that remain withoutdisappearing is derived.

An embodiment to which the present invention has been applied isexplained in further detail hereinafter. The BMD density of anitrogen-doped silicon wafer after the epitaxial process depends on 1)the nitrogen concentration, 2) the crystal thermal history, 3) thetemperature and time of a high-temperature heat treatment performed forelimination of natural oxide films in the epitaxial process, 4) thetemperature and time of pre-annealing performed before the epitaxialprocess, and 5) the oxygen concentration. Also, the BMD density of anitrogen-doped silicon wafer after the high-temperature annealingprocess depends on 1) the nitrogen concentration, 2) the crystal thermalhistory, 3) the thermal annealing rate during the high-temperatureannealing process, 4) the temperature annealing process, and 5) theoxygen concentration. Since the present invention provides a method forevaluating the influence of all of the above factors with respect to theBMD density, the conditions for obtaining an optimal BMD density can beselected.

The present invention provides the following, for example,

1) A method for deriving a relational equation relating the density ofthe radius of an oxygen precipitate introduced in a silicon crystaldoped with nitrogen at the time of crystal growth from the nitrogenconcentration and a cooling rate around 1100° C. during crystal growth,and predicting the oxygen precipitate density to be obtained after aheat treatment from the derived relational equation relating the oxygenprecipitate density to the radius, the oxygen concentration, and thetemperature process in epitaxial growth, and a method for obtaining anepitaxially grown wafer whose oxygen precipitate density is controlledto an appropriate density, using conditions predicted by the method.

2) A method for deriving a relational equation relating the density tothe radius of an oxygen precipitate introduced in a silicon crystaldoped with nitrogen at the time of crystal growth form the nitrogenconcentration and a cooling rate around 1100° C. during crystal growth,and predicting the oxygen precipitate density to be obtained after aheat treatment form the derived relational equation relating the oxygenprecipitate density to the radius, the oxygen concentration, and thetemperature process in annealing at a temperature of 1100° C. or more,and a method for obtaining a wafer annealed at a temperature of 1100° C.or more whose oxygen precipitate density has been controlled to anappropriate density, using conditions predicted by the method.

3) A method for obtaining an epitaxially grown wafer whose oxygenprecipitate density is 5×10⁸ units/cm³ or more, using conditionspredicted by the above method 1), when a cooling rate around 1100° C.during crystal growth is set to 0.76° C./minute or faster.

4) A method for obtaining an epitaxially grown wafer whose oxygenprecipitate density is 5×10⁸ units/cm³ or more, setting the maximumtemperature and time in the epitaxial growth process as predicted by theabove method 1), when a cooling rate around 1100° C. during crystalgrowth is set to 0.76° C./minute or faster.

5) A method for obtaining an epitaxially grown wafer whose oxygenprecipitate density is 5×10⁸ units/cm³ or more, setting a temperatureand time of a heat treatment performed before the epitaxial growthprocess as predicted by the above method 1), when a cooling rate around1100° C. during crystal growth is set to 0.76° C./minute or faster.

6) A method for obtaining a wafer annealed at a temperature of 1100° C.or more whose oxygen precipitate density is 5×10⁸ units/cm³ or more,using conditions predicted by the above method 2), when a cooling ratearound 1100° C. during crystal growth is set to 0.76° C./minute orfaster.

7) A method for obtaining a wafer annealed at a temperature of 1100° C.or more whose oxygen precipitate density is 5×10⁸ units/cm³ or more,setting a temperature and time of a heat treatment performed beforeannealing at a temperature of 1100° C. or more as predicted by the abovemethod 2), when a cooling rate around 1100° C. during crystal growth isset to 0.76° C./minute or faster.

8) A method for obtaining a wafer annealed at a temperature of 1100° C.or more whose oxygen precipitate density is 5×10⁸ units/cm³ or more,setting a thermal annealing rate in the thermal annealing process at700° C. or more and 900° C. or less in the annealing process to atemperature of 1100° C. or more as predicted by the above method 2),when a cooling rate around 1100° C. during crystal growth is set to0.76° C./minute or faster.

EMBODIMENTS

Hereinafter, the present invention is described further in detail basedon the embodiments.

Embodiment 1

An example of predicting the BMD density to be obtained in a case wherea wafer manufactured from a crystal whose cooling rate around 1100° C.during crystal growth is 3.5° C./minute undergoes an epitaxial growthprocess is shown. Here, the effects of the nitrogen concentration andthe temperature and time of a high-temperature pre-process (hereinafterreferred to as “hydrogen baking process” in some cases) performed toeliminate natural oxide films before the epitaxial growth are predictedby a method according to the present invention.

FIGS. 8, 9 and 10 show the relation of the BMD density vs. the holdingtime at a given pre-process temperature and nitrogen concentration, whenthe cooling rate around 1100° C. during crystal growth was set to 3.5°C./minute, the oxygen concentration at the time was set to 12.0×10¹⁷atoms/cm³, the thermal annealing time from 500° C. to the pre-processtemperature was set to 1 minute, and the pre-process temperature was setto each of 1150° C., 1200° C., and 1230° C. The calculation method is asfollows: the size distribution of as-grown oxygen precipitates isprovided as an initial value by Equation 4).

Then, the growth and disappearance of the nuclei having differing radiiin the temperature process in the epitaxial process are numericallycalculated by Equation 2) and 3).

As a result, the density of the BMD nuclei that remain withoutdisappearing is derived. Each of the contour lines in the figuresrepresents a BMD density, and some of the lines are provided with theirspecific BMD density values. From these figures, conditions forobtaining a BMD density of 5×10⁸ units/cm³ or more can be selected. Inthe case where the pre-process temperature and the epitaxial growthtemperature are the same, the total time of both processes correspondsto the time in FIGS. 8, 9 and 10. In the case where the temperatures aredifferent from each other, the above calculation may be done byincluding the pre-process and the epitaxial growth process in thetemperature process. However, in the case where the pre-processtemperature is higher than the epitaxial growth temperature, FIGS. 8, 9and 10 can be used as they are because the BMD density after theprocesses is determined at the stage of the pre-process.

Embodiment 2

An example in which the effects of the heat treatment temperature andtime of pre-annealing performed before an epitaxial growth process andthe nitrogen concentration on the BMD density are predicted by a methodaccording to the present invention is shown. The calculation method isthe same as that shown in Embodiment 1.

FIGS. 11, 12 and 13 show the relation of the BMD density vs. theannealing time and nitrogen concentration, when the cooling rate around1100° C. during crystal growth was set to 3.5° C./minute, the oxygenconcentration time from 500° C. in the epitaxial process was set to 1minute, the epitaxial temperature was set to 1200° C., the epitaxialprocess time was set to 1 minute, and the pre-annealing temperature wasset to each of 750° C., 800° C., and 850° C. Each of the contour linesin the figures represents a BMD density, and some of the lines areprovided with their specific BMD density values. From these figures, theconditions for obtaining the BMD density of 5×10⁸ units/cm³ or more canbe selected.

Embodiment 3

An example in which the effects of the heat treatment temperature andtime of pre-annealing performed before the high-temperature annealingprocess and the nitrogen concentration on the BMD density are predictedby a method according to the present invention is shown.

The cooling rate around 1100° C. during crystal growth was set to 3.5°C./minute, and the oxygen concentration was set to 12.0×10¹⁷ atoms/cm³.FIGS. 14 and 15 show the relation of the BMD density vs. the annealingtime and nitrogen concentration, when the pre-annealing temperature wasset to each of 750° C. and 800° C., respectively in case of the thermalannealing rate from 800° C. to 1000° C. was set to 10° C./minute, thethermal annealing rate from 1000° C. was set to 1100° C. was set to 2°C./minute, the thermal annealing rate from 1100° C. to 1200° C. was setto 1° C./minute, and the holding time at 1200° C. was set to 1 hour in ahigh-temperature annealing process. Each of the contour lines in thefigures represents a BMD density, and some of the lines are providedwith their specific BMD density values. From these figures, theconditions for obtaining the BMD density of 5×10⁸ units/cm³ or more canbe selected.

Embodiment 4

An example in which the effects of the thermal annealing rate in ahigh-temperature annealing process and the nitrogen concentration on theBMD density are predicted by a method according to the present inventionis shown. The result is shown in FIG. 16. The calculation method is thesame as that shown in Embodiment 1.

the cooling rate around 1100° C. during crystal growth was set to 3.5°C./minute, and the oxygen concentration was set to 12.0×10¹⁷ atoms/cm³.In the high-temperature annealing process, the thermal annealing ratefrom 800° C. to 1000° C. was set to the one shown in the figure, thethermal annealing rate from 1000° C. to 1100° C. was set to 2°C./minute, the thermal annealing rate from 1100° C. to 1200° C. was setto 1° C./minute, and the holding time at 1200° C. was set to 1 hour.Each of the contour lines in the figures represents a BMD density, andsome of the lines are provided with their specific BMD density values.From this figure, the conditions for obtaining the BMD density of 5×10⁸units/cm³ or more can be selected.

Next, the BMD density values of silicon wafers actually processed weremeasured and were compared with their predicted values according to thepresent invention (Embodiments 5, 6, 7 and 8). The experiments were donein accordance with (a) the manufacturing process for an epitaxial waferand (b) the manufacturing process for an annealed wafer as shown inFIGS. 17A and 17B, respectively. For reference, a general manufacturingprocess for a mirror finished wafer and a general manufacturing processfor an epi-wafer are shown in FIGS. 18A and 18B, respectively. In theprocess of a mirror finished wafer, from a selected polycrystallinesilicon (S312), a single crystal is manufactured (S314), a wafer cut outfrom this single crystal is wafer-processed (S316), is cleansed andinspected before shipping (S318), and is packed and shipped (S329). Inthis process, the cooling process in a predetermined temperature rangeat the time of manufacturing the single crystal is very important.Although a phenomenon occurring in this process is not clear, it isthrough to have an effect on the resulting BMD density, and thispredetermined temperature range can be regarded as a temperature rangein which the density of the oxygen precipitates increases. Although thetemperature range in which the density of the oxygen precipitatesincreases is thought to be determined by various conditions such asoxygen concentration, nitrogen concentration, temperature gradient,etc., it is thought to be around 1100° C. under normal conditions inwhich a single crystal is manufactured by the CZ method or MCZ method.If the cooling rate in such a temperature range is extremely small asdescribed above, a sufficient BMD density may not be obtained. Also, ina case where a heat treatment is performed in the processing step(S316), this heat treatment has an effect on the BMD density.

In the manufacturing process of an epi-wafer, from a polycrystallinesilicon selected in the same manner (S412), a single crystal ismanufactured (S414), a wafer cut out from this single crystal isprocessed (S416), an epi-layer is grown (S418), the wafer is cleansedand inspected before shipping (S420), and is packed and shipped (S422).As described above, the aforementioned cooling rate in the temperaturerange in which the density of the oxygen precipitates increases, theheat treatment in the wafer processing step (S416), and the temperatureconditions in the epi-layer growing step (S418) are thought to have aneffect on the resulting BMD density.

Embodiment 5

An example in which the effects of the heat treatment temperature andtime of pre-annealing performed before the epi-step on the BMD densitywere actually measured is compared with an example of its prediction bythe method according to the present invention. The result is shown inFIG. 19A. In the manufacturing process of an epitaxial wafer, first thesingle crystal growing step (S110) is performed, then the processingstep (S120) is performed, the epitaxial step (S140) is performed, andlastly, the cleansing step (S152) is performed, the manufacture anepitaxial wafer, as shown in FIG. 17A. More specifically, in the singlecrystal growing step (S110), a polycrystalline silicon is melted (S112),and a single crystal ingot is pulled up (S114) while the ingot is cooled(S116). Next, in the wafer processing step (S120), grinding crystaloutside step is performed (S122), ingot slicing processing is performed(S124), beveling of the sliced wafer is performed (S126), the surface ispolished by lapping (S128), etching (S130) and polishing (S132), thewafer is cleansed (S134), is pre-annealed (S136), and is cleansed(S138), to move onto the subsequent epitaxial step (S140). In theepitaxial step, hydrogen baking is performed (S142), and the wafer isepitaxially grown (S144). The wafer is finished with the aforementionedcleansing (S152). In this process, the ingot cooling step (S116), thepre-annealing step (S136) and the hydrogen baking step (S142) have aparticular effect on the BMD density. It is noted that the pre-annealingstep (S136) may be performed before the polishing step (S132). In thisexample, the cooling rate in a range around 1100° C. was set to 3.5°C./minute in the ingot cooling step (S116), and the conditions for thepre-annealing are shown in FIG. 19A. The hydrogen baking conditions inthe epitaxial step and other conditions are shown in FIG. 19B.

FIG. 19A shows the calculated and predicted values and the actualmeasured values of the BMD density. The highly correspond to each other,which shows that the above calculation is correct. Also, an evaluationin which a circle mark is given when the BMD density is 5×10⁸ units/cm³or more while a cross mark is given when it is less than this value isshown.

Embodiment 6

An example in which the effects of the temperature and time of thehydrogen baking in the epi-step on the BMD density were actuallymeasured is compared with an example of its prediction by the methodaccording to the present invention. The result is shown in FIG. 20A. Inthe manufacturing process of an epitaxial wafer, the ingot cooling step(S116), the pre-annealing step (S136) and the hydrogen baking step(S142) have a particular effect on the BMD density. In this example, thepre-annealing was not performed. The cooling rate in a range around1100° C. was set to 3.5° C./minute. The hydrogen baking conditions areshown in FIG. 20A. Other conditions in the epitaxial step are shown inFIG. 20B.

FIG. 20A shows the calculated and predicted values and the actualmeasured values of the BMD density. They highly correspond to eachother, which shows that the above calculation is correct. Also, anevaluation in which a circle mark is given when the BMD density is 5×10⁸units/cm³ or more while a cross mark is given when it is less than thisvalue is shown.

Embodiment 7

An example in which the effects of the heat treatment temperature andtime of pre-annealing performed before a high-temperature annealing stepon the BMD density were actually measured is compared with an example ofits prediction by the method according to the present invention. Theresult is shown in FIG. 21A. An annealed wafer was manufactured inaccordance with the aforementioned process (FIG. 17B). The manufacturingprocess of an annealed wafer consists of a single crystal growing step(S210), a processing step (S220), an annealing step (S240) and acleansing step (S252). More specifically, in the single crystal growingstep (S210), a polycrystalline silicon is melted (S212), and a singlecrystal ingot is pulled up (S214) while the ingot is cooled (S216).Next, in the processing step (S220), grinding crystal outside step isperformed (S222), ingot slicing processing is performed (S224), bevelingof the sliced wafer is performed (S226), the surface is polished bylapping (S228), etching (S230) and polishing (S232), the wafer iscleansed (S234), is pre-annealed (S236), and is cleansed (S238), to moveonto the subsequent annealing step (S242). The wafer is finished withthe aforementioned cleansing (S252). In this process, the ingot coolingstep (S216), the pre-annealing step (S236) and the annealing step (S242)have a particular effect on the BMD density.

The cooling rate in a range around 1100° C. was set to 3.5° C./minute,and in the annealing step, the high-temperature annealing was performedat 1200° C. for 1 hour, and the thermal annealing rate from 800° C. to1000° C. was set to 10° C./minute. The conditions for the pre-annealingand the other conditions in the manufacturing process of an annealedwafer are shown in FIG. 21B.

FIG. 21A shows calculated and predicted values and actual measuredvalues of the BMD density. They highly correspond to each other, whichshows that the above calculation is correct. Also, an evaluation inwhich a circle mark is given when the BMD density is 5×10⁸ units/cm³ ormore while a cross mark is given when it is less than this value isshown.

Embodiment 8

An example in which the effects of the thermal annealing rate in thehigh-temperature annealing step on the BMD density were actuallymeasured is compared with an example of its prediction by the methodaccording to the present invention. The result is shown in FIG. 22A. Inthe manufacturing process of an annealed wafer, the ingot cooling step(S216), the pre-annealing step (S236) and the annealing step (S242) havea particular effect on the BMD density. Thus, the cooling rate in arange around 1100° C. was set to 3.5° C./minute, and in the annealingstep, the high-temperature annealing was performed at 1200° C. for 1hour. The thermal annealing rate form 800° C. to 1000° C. in thehigh-temperature annealing and the other conditions in the manufacturingprocess of an annealed wafer are shown in FIG. 22B.

FIG. 22A shows the calculated and predicted values and the actualmeasured values of the BMD density. They highly correspond to eachother, which shows that the above calculation is correct. Also, anevaluation in which a circle mark is given when the BMD density is 5×10⁸units/cm³ or more while a cross mark is given when it is less than thisvalue is shown.

As described above, the present invention provides the following.

(1) A method comprising the steps of: deriving a relational equationrelating the density to the radius of an oxygen precipitate introducedin a silicon single crystal doped with nitrogen at the time of crystalgrowth from a nitrogen concentration and a cooling rate in a temperaturerange in which the density of the oxygen precipitates increases duringcrystal growth; and predicting the oxygen precipitate density to beobtained after a heat treatment from the derived relational equationrelating the oxygen precipitate density to the radius, the oxygenconcentration, and the temperature process of the heat treatment.

By the above method, the following silicon wafer can be provided. Thatis, it is a silicon wafer manufactured by deriving a relational equationrelating the density to the radius of an oxygen precipitate introducedin a silicon single crystal doped with nitrogen at the time of crystalgrowth from a nitrogen concentration and a cooling rate in a temperaturerange in which the density of the oxygen precipitates increases duringcrystal growth, predicting the oxygen precipitate density using theabove relational equation, nitrogen concentration, oxygen concentration,and a temperature process of a heat treatment, adjusting the nitrogenconcentration, the oxygen concentration, and the temperature process ofthe heat treatment so that the above predicted density becomes apredetermined value, and using the obtained nitrogen concentration,oxygen concentration, and temperature process of the heat treatment asmanufacturing conditions.

Meanwhile, nitrogen doping in the silicon single crystal can be done bydoping nitrogen or a compound containing nitrogen or the like in moltensilicon, and the nitrogen concentration in the silicon single crystalcan be determined by these doping conditions and the crystal growthconditions, etc. An oxygen precipitate introduced at the time of crystalgrowth is an oxide precipitated in the crystal grown form the moltensilicon and can include one grown to a measurable size. This size can beexpressed by using its radius, assuming that the precipitate isspherical. Also, the oxygen precipitate density can mean the number ofthe precipitates per unit volume of the crystal, and the nitrogenconcentration used here can mean the amount of nitrogen per unit volumeof the crystal. The temperature range in which the density of the oxygenprecipitates increases during crystal growth may be a temperature rangein which the density of the oxygen precipitates significantly increasesin a process in which the temperature is lowered along with crystalgrowth, for example, and its minimum and maximum temperature and thetemperature range may; be changed depending on various conditions.

(2) The method according to the above (1), wherein the temperature rangein which the density of the oxygen precipitates increases during crystalgrowth is around 1100° C.

Also, a silicon wafer can be provided which is the above silicon waferwherein the temperature range in which the density of the oxygenprecipitates increases during crystal growth is around 1100° C.

Here, “around 1100° C.” may mean a temperature range around 1100° C.

(3) The method according to the above (1) or (2), wherein thetemperature process of the heat treatment is a temperature process inepitaxial growth or a temperature process in annealing at a temperatureof 1100° C. or more.

(4) A method for deriving a relational equation relating the density tothe radius of an oxygen precipitate introduced in a silicon crystaldoped with nitrogen at the time of crystal growth from the nitrogenconcentration and the cooling rate around 1100° C. during crystalgrowth, and predicting the oxygen precipitate density to be obtainedafter the heat treatment from the derived relational equation relatingthe oxygen precipitate density to the radius, the oxygen concentration,and the temperature process in epitaxial growth.

(5) A method for deriving a relational equation relating the density tothe radius of an oxygen precipitate introduced in a silicon crystaldoped with nitrogen at the time of crystal growth from the nitrogenconcentration, and the cooling rate around 1100° C. during crystalgrowth, and predicting the oxygen precipitate density to be obtainedafter the heat treatment from the derived relational equation relatingthe oxygen precipitate density to the radius, the oxygen concentration,and the temperature process in annealing at a temperature of 1100° C. ormore.

(6) A method for manufacturing an epitaxially grown wafer by pulling upa silicon ingot by the CZ method or MCZ method, cutting out a siliconwafer from the ingot, pre-annealing the silicon wafer, performinghydrogen baking, and performing epitaxial growth on the silicon wafer,comprising the steps of: determining the density of oxygen precipitatesappropriate for an intended application of the epitaxially grown wafer;and, based on an oxygen and nitrogen concentration obtained, determininga cooling rate at the time of pulling up the silicon ingot, antemperature and holding time of pre-annealing, and a temperature andholding time of hydrogen baking by a predetermined relational equation.

(7) A method for determining the density of oxygen precipitatesappropriate for application of an epitaxially grown wafer or ahigh-temperature annealed silicon wafer to be manufactured by pulling upa silicon ingot by the CZ method or MCZ method, cutting out a siliconwafer from the ingot, and pre-annealing the silicon wafer, and, based onthe oxygen and nitrogen concentration, determining the cooling rate atthe time of pulling up the silicon ingot, the temperature and holdingtime of pre-annealing, and the temperature and holding time of hydrogenbaking for the epitaxially grown wafer or the thermal annealing rate ina predetermined temperature range of high-temperature annealing for thehigh-temperature annealed silicon wafer by a predetermined relationalequation, so that the determined density of oxygen precipitates isobtained.

(8) A wafer manufactured under the conditions determined by the abovemethod (7).

Here, the predetermined relational equation may include a relationequation relating the density to the radius of an oxygen precipitateintroduced at the time of crystal growth. It may also include a relationequation in which the nitrogen concentration and the cooling rate in atemperature range in which the density of the oxygen precipitatesincreases during crystal growth can be used as variables.

(9) A method for manufacturing a product silicon wafer by pulling up asilicon ingot by the CZ method or MCZ method, cutting out a siliconwafer from the ingot, pre-annealing the silicon wafer, and performinghigh-temperature annealing, comprising the step of: determining thedensity of oxygen precipitates appropriate for an intended applicationof the product silicon wafer; and, based on an oxygen and nitrogenconcentration obtained, determining a cooling rate at the time ofpulling up the silicon ingot, a temperature and holding time ofpre-annealing, and a thermal annealing rate in a predeterminedtemperature range of high-temperature annealing by a predeterminedrelational equation.

Here, the predetermined temperature range of high-temperature annealingmay include a temperature range that can have an effect on the increaseof the oxygen precipitate density. The specific temperature range isdetermined by various conditions.

(10) A program for predicting the density of oxygen precipitates in asilicon wafer, prompting for input of a cooling rate in a temperaturerange in which the density of oxygen precipitates introduced at the timeof crystal growth in a silicon single crystal as a raw material of thesilicon wafer increases, a nitrogen concentration in the silicon singlecrystal, and/or nitrogen concentration, calculating the oxygenprecipitate density to be obtained after a heat treatment by apredetermined relational equation expressing the density to the radiusof the oxygen precipitate introduced at the time of crystal growth byusing data of a temperature process that the silicon wafer undergoes,and outputting a result of the calculation.

(11) A recording medium recording the program according to the above(9).

(12) A wafer manufactured by the manufacturing method according to theabove (6) or (7).

(13) An epitaxially grown wafer manufactured by a method formanufacturing an epitaxially grown wafer comprising a step ofcontrolling various conditions by using the prediction method accordingto any one of the above (1) to (3), so that a predetermined oxygenprecipitate density is obtained.

Here, the various conditions to be controlled my include conditions thatcan have an effect on an increase of the oxygen precipitate density. Forexample, they can include temperature conditions such as the thermalannealing rate, the cooling rate, the holding temperature, holding timeetc. in one or more steps in the manufacture of a silicon wafer, thecomponent conditions such as the material components and othercomponents, and the manufacturing conditions such as the pulling rate,the supply rate, atmosphere etc.

(14) A silicon wafer whose oxygen precipitate density is controlled toan appropriate density based on the conditions predicted by the methodaccording to the above (1), (2) or (4).

(15) A wafer annealed at a temperature of 1100° C. or more whose oxygenprecipitate density is controlled to an appropriate density based on theconditions predicted by the method according to the above (5).

(16) A silicon wafer whose oxygen precipitate density is 5×10⁸ units/cm³or more based on the conditions predicted by the method according to theabove (1), (2) or (4), setting the cooling rate around 1100° C. duringcrystal growth to 0.76° C./minute or faster. Also, it is possible toprovide a method for making the oxygen precipitate density in a siliconwafer to be manufactured 5×10⁸ units/cm³ or more by setting the coolingrate around 1100° C. during crystal growth to 0.76° C./minute or faster,and using conditions predicted by the method according to the above (1),(2) or (4).

(17) An epitaxially grown wafer whose oxygen precipitate density is5×10⁸ units/cm³ or more, setting the maximum temperature and time in anepitaxial growth process as predicted by the above method (4), when thecooling rate around 1100° C. during crystal growth is set to 0.76°C./minute or faster.

(18) An epitaxially grown wafer whose oxygen precipitate density is5×10⁸ units/cm³ or more, setting the temperature and time of a heattreatment performed before an epitaxial growth process as predicted bythe above method (4), when the cooling rate around 1100° C. duringcrystal growth is set to 0.76° C./minute or faster.

(19 ) A wafer annealed at a temperature of 1100° C. or more whose oxygenprecipitate density is 5×10⁸ units/cm³ or more, using the conditionspredicted by the above method (5), when the cooling rate around 1100° C.during crystal growth is set to 0.76° C./minute or faster.

(20) A wafer annealed at a temperature of 1100° C. or more whose oxygenprecipitate density is 5×10⁸ units/cm³ or more, setting the temperatureand time of a heat treatment performed before annealing at a temperatureof 1100° C. or more as predicted by the above method (5), when thecooling rate around 1100° C. during crystal growth is set to 0.76°C./minute or faster.

(21) A wafer annealed at a temperature of 1100° C. or more whose oxygenprecipitate density is 5×10⁸ units/cm³ or more, setting the thermalannealing rate in the thermal annealing process at 700° C. or more and900° C. or less in the annealing process to a temperature of 1100° C. ormore as predicted by the above method (5), when the cooling rate around1100° C. during crystal growth is set to 0.76° C./minute or faster.

It is to be understood that the present invention is not limited by theembodiments described here.

to control the resistance of a CZ silicon crystal, B, P, As, Sb etc. aswell as oxygen and nitrogen are doped in the CZ silicon crystal. It iswell known that increasing the doping concentration will have an effecton the oxygen precipitate. The present invention can be applied to ap-type crystal is low, that is, in which the resistivity is 0.5 Ωcm ormore. Predictions concerning the oxygen precipitates in a crystal havinga lower resistivity can be made accurately as described in the presentinvention by evaluating the as-grown nucleus distribution at eachresistivity or doping concentration in accordance with the procedures ofthe present invention.

1. A method comprising the steps of: deriving a relational equationrelating the density to the radius of an oxygen precipitate introducedin a silicon single crystal doped with nitrogen at the time of crystalgrowth from the nitrogen concentration and the cooling rate in atemperature range in which the density of the oxygen precipitates duringcrystal growth; and predicting the oxygen precipitate density to beobtained after a heat treatment from the derived relational equationrelating the oxygen precipitate density to the radius, the oxygenconcentration, and the temperature process of the heat treatment.
 2. Themethod according to claim 1, wherein the temperature range in which thedensity of the oxygen precipitates increases during crystal growth isaround 1100° C.
 3. A program for predicting the density of oxygenprecipitates in a silicon wafer and a recording medium recording theprogram, the program prompting for input of a cooling rate in atemperature range in which the density of oxygen precipitates introducedat the time of crystal growth in a silicon single crystal as a rawmaterial of the silicon wafer increases, the nitrogen concentration inthe silicon single crystal, and/or nitrogen concentration, calculatingthe oxygen precipitate density to be obtained after a heat treatment bya predetermined relational equation relating the density to the radiusof the oxygen precipitate introduced at the time of crystal growth byusing data of a temperature process that the silicon wafer undergoes,and outputting a result of the calculation.
 4. An epitaxially grownwafer or a high-temperature annealed silicon wafer to be manufactured bypulling up a silicon ingot the CZ method or MCZ method, cutting out asilicon wafer from the into, and pre-annealing the silicon wafer.wherein the density of oxygen precipitates appropriate for an intendedapplication of the epitaxially grown wafer or the high-temperatureannealed silicon wafer to be manufactured is determined. wherein, basedon the oxygen and nitrogen concentration, a cooling rate at the time ofpulling up the silicon ingot, a temperature and holding time ofpre-annealing, and a temperature and holding time of hydrogen baking forthe epitaxially grown wafer or a thermal annealing rate in apredetermined temperature range of high-temperature annealing for thehigh-temperature annealed silicon wafer are determined by apredetermined relational equation, so that the determined density ofoxygen precipitates is obtained, and wherein the wafer is manufacturedunder determined conditions.
 5. A silicon wafer whose oxygen precipitatedensity is controlled to an appropriate density based on conditionspredicted by the method according to claim
 1. 6. A silicon wafer whoseoxygen precipitate density is 5×10⁸ units/cm³ or more based onconditions predicted by the method according to claim 1, setting acooling rate around 1100° C. during crystal growth to 0.76° C./minute orfaster.
 7. A silicon wafer whose oxygen precipitate density iscontrolled to an appropriate based on conditions predicted by the methodaccording to claim
 2. 8. A silicon wafer whose oxygen precipitatedensity is 5×10⁸ units/cm³ or more based on conditions predicted by themethod according to claim 2, setting a cooling rate around 1100° C.during crystal growth to 0.76° C./minute or faster.